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 A274042 Numbers n such that n - 53, n - 1, n + 1, n + 53 are consecutive primes. 1
 9401700, 64312710, 78563130, 83494350, 92978310, 101520540, 111105090, 121631580, 136765860, 138330780, 139027950, 145673850, 157008390, 163050090, 166418280, 169288530, 170473410, 177920850, 198963210, 200765250, 213504870, 220428600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is a subsequence of A014574 (average of twin prime pairs), A249674 (divisible by 30) and A256753. The numbers n - 53 and n + 1 belong to A204665 (p such that p + 52 is the next prime). The numbers n - 53 and n ­- 1 belong to primes p such that p + 54 is prime. LINKS Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Twin Primes EXAMPLE 9401700 is the average of the four consecutive primes 9401647, 9401699, 9401701, 9401753. 64312710 is the average of the four consecutive primes 64312657, 64312709, 64312711, 64312763. MATHEMATICA Select[Partition[Prime[Range[122*10^5]], 4, 1], Differences[#]=={52, 2, 52}&][[All, 2]]+1 (* Harvey P. Dale, Mar 07 2018 *) PROG (Python) from sympy import isprime, prevprime, nextprime for i in range(0, 250000001, 6): ..if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-53 and nextprime(i+1) == i+53: print (i, end=', ') CROSSREFS Cf. A014574, A077800 (twin primes), A249674, A256753. Sequence in context: A328207 A069376 A281570 * A066703 A270994 A162030 Adjacent sequences:  A274039 A274040 A274041 * A274043 A274044 A274045 KEYWORD nonn AUTHOR Karl V. Keller, Jr., Jun 07 2016 STATUS approved

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Last modified August 12 20:18 EDT 2022. Contains 356077 sequences. (Running on oeis4.)